svc_norm.r

This is an EFA for the ratings of the self on all items. Only 70 of the 77 have totally complete data, and to be conservative, I’m just looking at those 70. We don’t lose too much without those 7 and it’s easier to satisfy assumptions of EFA without missing data. Haven’t looked closely at what they’re missing yet though.

Descriptives

These histograms by themselves tell a really interesting story – you can see that there is a some overlap between Acc and Cont ratings, but some items distinguish between them. These line up with a lot of our a priori ideas – see anger and jealousy. Pretty cool.

Aside from the status items, you also can see the scores on depression and substance use, among other things. Keep in mind the middle 2 CES_D items are reverse coded. SES ladder is mostly between 3-7 on a 9 point scale.

desc	skew	pval	mean	sd
insecure_Self	-0.0283501	0.9019713	3.490000	1.7551943
daring_Self	-0.0369397	0.8725091	3.250000	1.4728177
stubborn_Self	-0.0579809	0.8012135	3.490000	1.5858911
leader_Self	0.1027514	0.6559274	3.310000	1.5419717
outgoing_Self	-0.1224289	0.5958376	3.550000	1.7602514
popular_Self	0.1436750	0.5359458	3.292929	1.5859879
trendy_Self	-0.1445669	0.5334386	3.454546	1.5536181
athletic_Self	-0.1573981	0.4961474	3.540000	1.6231905
plain_Self	0.1663235	0.4742817	3.232323	1.5896880
pushover_Self	0.1733206	0.4561013	3.010101	1.6567423
confident_Self	-0.1805505	0.4377608	3.686869	1.5626147
flirty_Self	0.1910091	0.4120430	3.121212	1.6242595
lonely_Self	0.2134421	0.3580291	3.170000	1.6517820
jealous_Self	0.2166837	0.3509063	2.900000	1.4389952
admired_Self	-0.2248039	0.3334858	3.610000	1.4832056
loner_Self	0.2408992	0.3007352	3.120000	1.7249213
awkward_Self	-0.2509980	0.2813861	3.600000	1.6817499
poor_Self	0.2688930	0.2493376	2.840000	1.5486716
dependent_Self	-0.3042124	0.1941856	3.650000	1.4310764
risky_Self	0.3162972	0.1776644	2.900000	1.4459976
shy_Self	-0.3172830	0.1763672	3.850000	1.7196135
cool_Self	-0.3321158	0.1595970	3.767677	1.4971284
depressed_Self	0.3563828	0.1324318	2.989899	1.6751177
social_Self	-0.3708593	0.1164910	3.910000	1.6023657
selfish_Self	0.4277253	0.0737972	2.646465	1.4308063
boring _Self	0.4287829	0.0718664	2.770000	1.5166084
patient_Self	-0.4599712	0.0557251	4.141414	1.3477881
studious_Self	-0.4838010	0.0440607	4.370000	1.2764772
adventurous_Self	-0.4871470	0.0427308	3.960000	1.4696938
genuine_Self	-0.5502226	0.0235596	4.730000	1.0996326
considerate_Self	-0.5567995	0.0221008	4.810000	1.0317681
bossy_Self	0.5578755	0.0218702	2.610000	1.5034976
lazy_Self	0.5746806	0.0190660	2.636364	1.5349968
grumpy_Self	0.5781332	0.0184309	2.646465	1.5139699
caring_Self	-0.6049512	0.0137084	4.740000	1.0882290
attractive_Self	-0.6192752	0.0118559	4.090000	1.3640033
comforting_Self	-0.6278347	0.0108637	4.160000	1.3905889
funny_Self	-0.6287765	0.0107594	4.210000	1.2815316
rule-follower_Self	-0.6307734	0.0105414	4.300000	1.3521401
controlling_Self	0.6337901	0.0102200	2.600000	1.4839206
calm_Self	-0.6507185	0.0088741	4.444444	1.1712737
humble_Self	-0.6776478	0.0064745	4.360000	1.2351747
helpful_Self	-0.6789290	0.0063877	4.780000	1.0596359
agressive_Self	0.7324172	0.0037556	2.333333	1.4356965
giving_Self	-0.7483863	0.0030331	4.560000	1.2578642
snobby_Self	0.7502175	0.0031001	2.323232	1.4765395
angry_Self	0.7731570	0.0023127	2.480000	1.4666667
honest_Self	-0.7748193	0.0023727	4.595960	1.2030505
motivated_Self	-0.7847003	0.0021295	4.444444	1.2874767
rude_Self	0.8024367	0.0016730	2.170000	1.2953296
mean_Self	0.8178574	0.0014088	2.230000	1.4131775
nice_Self	-0.8676875	0.0008039	4.880000	0.9773185
welcoming_Self	-0.8746451	0.0007429	4.550000	1.2007994
friendly_Self	-0.8770667	0.0007227	4.650000	1.2583057
ugly_Self	0.9027683	0.0005391	2.390000	1.4347421
sympathetic_Self	-0.9293323	0.0004210	4.525252	1.3041804
trustworthy_Self	-1.0070150	0.0001616	4.830000	1.0546195
smart_Self	-1.0217586	0.0001552	4.918367	0.9809891
fair_Self	-1.0710441	0.0000764	4.630000	1.2605514
fake_Self	1.0872091	0.0000632	1.930000	1.1997895
loyal_Self	-1.1144612	0.0000458	4.770000	1.1964172
respectful_Self	-1.2988493	0.0000052	4.870000	1.0885539

The plot below seems to indicate that a good number of people consider themselves high status in both ways (all responses in the top right quadrant). There doesn’t seem to be perfect separation between the two. However, note that the bottom left quadrant reflects responses from people that think neither type of status describes them well (31 people). Also note that the overlap group is only comprises 13 people. Number of primarily accepted status = 39, and primarily controversial status participants = 15.

Controversial versus Accepted Status Frequencies

Cont_v_Acc	1	2	3	4	5	6
1	11	6	5	7	7	6
2	2	1	2	6	3	3
3	1	1	2	3	4	0
4	1	1	5	1	5	0
5	1	1	2	3	3	0
6	3	0	1	0	0	1

We want to keep all the prosocial items we can, so let’s see what correlates with it and just remove those items from the factor analysis. Then we can see what else sticks together, and use that as the second one.

##         risky_Self           shy_Self        daring_Self 
##        -0.03381114        -0.05986764         0.06750512 
##      stubborn_Self        flirty_Self     dependent_Self 
##        -0.07525814         0.09126158        -0.09259563 
##        trendy_Self         plain_Self   controlling_Self 
##         0.13226106        -0.13549504        -0.13905925 
##      outgoing_Self          cool_Self        lonely_Self 
##         0.15062385         0.15787746        -0.16395309 
## rule-follower_Self       awkward_Self      athletic_Self 
##         0.16834631        -0.16862502         0.18087389 
##        leader_Self      insecure_Self         bossy_Self 
##         0.19548830        -0.19982895        -0.21179868 
##   adventurous_Self      pushover_Self         loner_Self 
##         0.21866287        -0.21886119        -0.22048685 
##        social_Self       popular_Self     depressed_Self 
##         0.22651835         0.22707536        -0.23225008 
##       admired_Self          poor_Self     confident_Self 
##         0.23982741        -0.25653584         0.26793293 
##       jealous_Self          ugly_Self     agressive_Self 
##        -0.27351833        -0.27552265        -0.28895723 
##       boring _Self         funny_Self    comforting_Self 
##        -0.29080782         0.29730289         0.29954552 
##    attractive_Self       selfish_Self          rude_Self 
##         0.30163030        -0.30956400        -0.30957320 
##    respectful_Self         angry_Self          calm_Self 
##         0.31089893        -0.31100697         0.31631639 
##       patient_Self         loyal_Self        humble_Self 
##         0.31727518         0.32366047         0.32510420 
##        grumpy_Self     motivated_Self      studious_Self 
##        -0.32839170         0.32983626         0.33414129 
##        snobby_Self          fake_Self        giving_Self 
##        -0.34542901        -0.35220158         0.37118279 
##          mean_Self          fair_Self   sympathetic_Self 
##        -0.37379551         0.39606736         0.39625965 
##       genuine_Self     welcoming_Self      friendly_Self 
##         0.41450943         0.41602265         0.41877785 
##   considerate_Self        caring_Self          nice_Self 
##         0.43528960         0.44409166         0.47053254 
##   trustworthy_Self 
##         0.48584338

Self Ratings

Best predictors of status

First thing, let’s see what items are best at predicting status using regularized regression for multinomial responses. This uses cross validation to give us the set of predictors that leads to the best out-of-sample prediction (least error).

The first plot shows how prediction error varies as a function of the number of parameters in the model, and how much weight each gets (the size of the coefficient).

The second set of plots actually show the size of each coefficient predicting both types of status as the constraint parameter, lambda, is tightened (left-to-right).

This table shows all the non-zero coefficients

Best predictors of self-report status

xName	ContStat	AccStat
(Intercept)	1.424	2.787
admired_Self	0.079	0.074
agressive_Self	0.065	0.049
angry_Self	0.140	-0.105
awkward_Self	0.016	-0.023
cool_Self	0.047	0.052
grumpy_Self	0.043	-0.043
jealous_Self	0.086	-0.016
leader_Self	-0.012	0.102
mean_Self	0.035	0.005
poor_Self	0.019	-0.113
popular_Self	0.020	0.107
risky_Self	0.047	-0.044
rude_Self	0.128	-0.019
rulefollower_Self	-0.054	0.061
selfish_Self	0.003	-0.001
shy_Self	0.033	-0.094
snobby_Self	0.014	0.008
social_Self	0.040	0.177
studious_Self	-0.029	0.002
trendy_Self	0.055	0.130

If we were merely trying to predict status from a future data set containing these same items, the above table would be the best subset to use. I’ll come back to these later, because I think they’ll be useful in our final item selection.

While we’re interested in predicting status, we’re not actually asking about status. Rather, we’re asking about traits that we think relate to status. So while the above set of items might tell us who is likely to have one or the other kind of status, in the context of an fMRI analysis it would be hard to argue that activity observed during self evaluation of these traits is some measure of status-related brain activity.

EFA to look at latent constructs

The more traditional approach would be to use EFA. What we hope to get is 2 factors the correspond to Accepted High Status and Controversial High Status.

However, the scree plot shows very clearly a 4 factor solution will account for most of the variance, with no real gain if we increase beyond 4.

## Factor Analysis using method =  pa
## Call: fa(r = select(selfRateDat, -matches("SelfPop")), nfactors = 3, 
##     rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                    item   PA3   PA1   PA2   h2   u2 com
## insecure_Self        31 -0.86  0.09  0.20 0.72 0.28 1.1
## lonely_Self          35 -0.84  0.14  0.28 0.69 0.31 1.3
## depressed_Self       19 -0.82  0.10  0.29 0.69 0.31 1.3
## loner_Self           36 -0.79 -0.03  0.09 0.64 0.36 1.0
## awkward_Self          7 -0.78  0.16  0.26 0.59 0.41 1.3
## confident_Self       13  0.77  0.20  0.15 0.74 0.26 1.2
## trendy_Self          59  0.76  0.05  0.25 0.67 0.33 1.2
## shy_Self             52 -0.73  0.22 -0.02 0.49 0.51 1.2
## popular_Self         45  0.72  0.23  0.27 0.73 0.27 1.5
## social_Self          55  0.71  0.22  0.27 0.71 0.29 1.5
## plain_Self           43 -0.67  0.10  0.09 0.42 0.58 1.1
## flirty_Self          22  0.64  0.04  0.27 0.51 0.49 1.4
## boring _Self          8 -0.64 -0.03  0.23 0.46 0.54 1.3
## admired_Self          1  0.62  0.25  0.36 0.65 0.35 2.0
## outgoing_Self        41  0.62  0.14  0.24 0.52 0.48 1.4
## attractive_Self       6  0.61  0.33  0.22 0.63 0.37 1.8
## cool_Self            16  0.60  0.27  0.41 0.68 0.32 2.2
## ugly_Self            61 -0.59 -0.18  0.17 0.47 0.53 1.4
## leader_Self          34  0.57  0.12  0.32 0.49 0.51 1.7
## pushover_Self        46 -0.57  0.05  0.22 0.35 0.65 1.3
## adventurous_Self      2  0.50  0.29  0.33 0.51 0.49 2.4
## funny_Self           24  0.49  0.30  0.15 0.43 0.57 1.9
## poor_Self            44 -0.46 -0.22  0.33 0.45 0.55 2.3
## daring_Self          17  0.43  0.08  0.38 0.36 0.64 2.0
## athletic_Self         5  0.31  0.18  0.10 0.17 0.83 1.9
## nice_Self            40 -0.05  0.84 -0.10 0.73 0.27 1.0
## considerate_Self     14 -0.15  0.83 -0.10 0.69 0.31 1.1
## helpful_Self         28  0.08  0.79  0.03 0.66 0.34 1.0
## genuine_Self         25 -0.03  0.77 -0.02 0.58 0.42 1.0
## caring_Self          11  0.04  0.76 -0.02 0.59 0.41 1.0
## loyal_Self           37 -0.12  0.74  0.00 0.51 0.49 1.1
## friendly_Self        23  0.13  0.72 -0.02 0.59 0.41 1.1
## trustworthy_Self     60  0.11  0.72 -0.04 0.58 0.42 1.0
## giving_Self          26  0.04  0.71  0.03 0.52 0.48 1.0
## sympathetic_Self     58  0.00  0.71 -0.06 0.52 0.48 1.0
## welcoming_Self       62  0.11  0.68 -0.15 0.58 0.42 1.2
## fair_Self            20  0.05  0.59 -0.20 0.46 0.54 1.2
## respectful_Self      47  0.00  0.57 -0.06 0.35 0.65 1.0
## humble_Self          30 -0.25  0.56 -0.20 0.38 0.62 1.7
## calm_Self            10  0.15  0.55 -0.15 0.44 0.56 1.3
## honest_Self          29  0.20  0.50 -0.14 0.40 0.60 1.5
## rule-follower_Self   50 -0.20  0.47 -0.05 0.22 0.78 1.4
## studious_Self        57 -0.10  0.47 -0.05 0.22 0.78 1.1
## motivated_Self       39  0.16  0.46 -0.03 0.29 0.71 1.2
## smart_Self           53  0.03  0.45 -0.07 0.23 0.77 1.1
## comforting_Self      12  0.34  0.44  0.00 0.40 0.60 1.9
## patient_Self         42  0.13  0.43 -0.27 0.36 0.64 1.9
## controlling_Self     15  0.23 -0.01  0.74 0.61 0.39 1.2
## snobby_Self          54  0.02 -0.29  0.72 0.68 0.32 1.3
## bossy_Self            9  0.23 -0.14  0.72 0.62 0.38 1.3
## angry_Self            4 -0.32 -0.09  0.71 0.64 0.36 1.4
## rude_Self            49  0.04 -0.26  0.70 0.62 0.38 1.3
## mean_Self            38  0.01 -0.32  0.70 0.67 0.33 1.4
## grumpy_Self          27 -0.42 -0.05  0.66 0.62 0.38 1.7
## agressive_Self        3  0.13 -0.24  0.66 0.55 0.45 1.4
## selfish_Self         51 -0.10 -0.27  0.60 0.52 0.48 1.5
## jealous_Self         32 -0.39  0.02  0.56 0.44 0.56 1.8
## lazy_Self            33 -0.15 -0.16  0.49 0.33 0.67 1.4
## fake_Self            21 -0.14 -0.40  0.48 0.51 0.49 2.1
## stubborn_Self        56 -0.06  0.12  0.47 0.21 0.79 1.2
## risky_Self           48  0.22 -0.05  0.46 0.27 0.73 1.4
## dependent_Self       18 -0.28  0.18  0.39 0.19 0.81 2.3
## 
##                         PA3   PA1  PA2
## SS loadings           12.44 11.27 7.84
## Proportion Var         0.20  0.18 0.13
## Cumulative Var         0.20  0.38 0.51
## Proportion Explained   0.39  0.36 0.25
## Cumulative Proportion  0.39  0.75 1.00
## 
##  With factor correlations of 
##      PA3   PA1   PA2
## PA3 1.00  0.31  0.04
## PA1 0.31  1.00 -0.19
## PA2 0.04 -0.19  1.00
## 
## Mean item complexity =  1.4
## Test of the hypothesis that 3 factors are sufficient.
## 
## The degrees of freedom for the null model are  1891  and the objective function was  72.05 with Chi Square of  5583.84
## The degrees of freedom for the model are 1708  and the objective function was  34.22 
## 
## The root mean square of the residuals (RMSR) is  0.06 
## The df corrected root mean square of the residuals is  0.06 
## 
## The harmonic number of observations is  99 with the empirical chi square  1373.9  with prob <  1 
## The total number of observations was  100  with MLE Chi Square =  2583.27  with prob <  6.4e-39 
## 
## Tucker Lewis Index of factoring reliability =  0.727
## RMSEA index =  0.1  and the 90 % confidence intervals are  0.066 0.077
## BIC =  -5282.36
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy             
##                                                 PA3  PA1  PA2
## Correlation of scores with factors             0.99 0.98 0.98
## Multiple R square of scores with factors       0.97 0.96 0.96
## Minimum correlation of possible factor scores  0.95 0.93 0.91

## Factor Analysis using method =  pa
## Call: fa(r = select(selfRateDat, -matches("SelfPop")), nfactors = 2, 
##     rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                    item   PA1   PA2    h2   u2 com
## popular_Self         45  0.85  0.02 0.730 0.27 1.0
## social_Self          55  0.84  0.01 0.714 0.29 1.0
## confident_Self       13  0.84  0.09 0.740 0.26 1.0
## trendy_Self          59  0.83 -0.10 0.674 0.33 1.0
## cool_Self            16  0.81 -0.07 0.641 0.36 1.0
## admired_Self          1  0.80 -0.05 0.635 0.37 1.0
## attractive_Self       6  0.76  0.12 0.620 0.38 1.1
## outgoing_Self        41  0.73 -0.04 0.520 0.48 1.0
## flirty_Self          22  0.72 -0.14 0.511 0.49 1.1
## loner_Self           36 -0.71 -0.15 0.567 0.43 1.1
## leader_Self          34  0.70 -0.12 0.482 0.52 1.1
## insecure_Self        31 -0.69 -0.14 0.537 0.46 1.1
## adventurous_Self      2  0.69  0.01 0.472 0.53 1.0
## shy_Self             52 -0.63  0.13 0.383 0.62 1.1
## lonely_Self          35 -0.62 -0.17 0.452 0.55 1.1
## depressed_Self       19 -0.62 -0.21 0.467 0.53 1.2
## funny_Self           24  0.61  0.15 0.420 0.58 1.1
## daring_Self          17  0.58 -0.20 0.342 0.66 1.2
## awkward_Self          7 -0.57 -0.13 0.371 0.63 1.1
## plain_Self           43 -0.56 -0.04 0.329 0.67 1.0
## ugly_Self            61 -0.53 -0.31 0.439 0.56 1.6
## boring _Self          8 -0.51 -0.25 0.366 0.63 1.4
## comforting_Self      12  0.44  0.36 0.383 0.62 1.9
## pushover_Self        46 -0.43 -0.17 0.238 0.76 1.3
## athletic_Self         5  0.39  0.09 0.169 0.83 1.1
## mean_Self            38  0.20 -0.79 0.607 0.39 1.1
## snobby_Self          54  0.23 -0.78 0.608 0.39 1.2
## rude_Self            49  0.25 -0.74 0.547 0.45 1.2
## nice_Self            40  0.15  0.73 0.587 0.41 1.1
## considerate_Self     14  0.05  0.71 0.525 0.48 1.0
## fake_Self            21 -0.05 -0.70 0.500 0.50 1.0
## agressive_Self        3  0.31 -0.69 0.503 0.50 1.4
## selfish_Self         51  0.07 -0.69 0.461 0.54 1.0
## welcoming_Self       62  0.24  0.65 0.538 0.46 1.3
## bossy_Self            9  0.47 -0.65 0.535 0.47 1.8
## angry_Self            4 -0.03 -0.64 0.416 0.58 1.0
## fair_Self            20  0.14  0.62 0.433 0.57 1.1
## genuine_Self         25  0.18  0.61 0.441 0.56 1.2
## caring_Self          11  0.24  0.60 0.470 0.53 1.3
## helpful_Self         28  0.31  0.60 0.512 0.49 1.5
## sympathetic_Self     58  0.18  0.59 0.420 0.58 1.2
## trustworthy_Self     60  0.29  0.59 0.492 0.51 1.5
## friendly_Self        23  0.32  0.58 0.498 0.50 1.5
## humble_Self          30 -0.16  0.58 0.327 0.67 1.2
## grumpy_Self          27 -0.14 -0.57 0.376 0.62 1.1
## loyal_Self           37  0.10  0.57 0.350 0.65 1.1
## calm_Self            10  0.24  0.56 0.421 0.58 1.3
## patient_Self         42  0.14  0.56 0.361 0.64 1.1
## controlling_Self     15  0.51 -0.56 0.475 0.53 2.0
## giving_Self          26  0.25  0.53 0.389 0.61 1.4
## lazy_Self            33  0.01 -0.52 0.266 0.73 1.0
## honest_Self          29  0.28  0.51 0.387 0.61 1.5
## respectful_Self      47  0.14  0.49 0.288 0.71 1.2
## poor_Self            44 -0.36 -0.46 0.405 0.60 1.9
## jealous_Self         32 -0.14 -0.44 0.236 0.76 1.2
## smart_Self           53  0.13  0.41 0.202 0.80 1.2
## studious_Self        57  0.02  0.40 0.162 0.84 1.0
## motivated_Self       39  0.27  0.39 0.263 0.74 1.8
## rule-follower_Self   50 -0.08  0.39 0.150 0.85 1.1
## risky_Self           48  0.38 -0.38 0.242 0.76 2.0
## stubborn_Self        56  0.17 -0.28 0.088 0.91 1.6
## dependent_Self       18 -0.05 -0.18 0.039 0.96 1.2
## 
##                         PA1   PA2
## SS loadings           13.53 13.19
## Proportion Var         0.22  0.21
## Cumulative Var         0.22  0.43
## Proportion Explained   0.51  0.49
## Cumulative Proportion  0.51  1.00
## 
##  With factor correlations of 
##      PA1  PA2
## PA1 1.00 0.17
## PA2 0.17 1.00
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  1891  and the objective function was  72.05 with Chi Square of  5583.84
## The degrees of freedom for the model are 1768  and the objective function was  41.33 
## 
## The root mean square of the residuals (RMSR) is  0.1 
## The df corrected root mean square of the residuals is  0.1 
## 
## The harmonic number of observations is  99 with the empirical chi square  3502.54  with prob <  8.8e-117 
## The total number of observations was  100  with MLE Chi Square =  3147.64  with prob <  1.2e-80 
## 
## Tucker Lewis Index of factoring reliability =  0.59
## RMSEA index =  0.115  and the 90 % confidence intervals are  0.083 0.093
## BIC =  -4994.3
## Fit based upon off diagonal values = 0.91
## Measures of factor score adequacy             
##                                                 PA1  PA2
## Correlation of scores with factors             0.99 0.98
## Multiple R square of scores with factors       0.97 0.96
## Minimum correlation of possible factor scores  0.95 0.93

Here’s the raw output, if you like, but see below for a prettier table. Notice the factors are allowed to correlate.

## Factor Analysis using method =  pa
## Call: fa(r = select(selfRateDat, -matches("SelfPop")), nfactors = 4, 
##     rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                    item   PA3   PA1   PA2   PA4   h2   u2 com
## depressed_Self       19  0.91  0.11  0.16  0.16 0.76 0.24 1.2
## insecure_Self        31  0.89  0.09  0.10  0.05 0.75 0.25 1.1
## lonely_Self          35  0.83  0.13  0.23 -0.05 0.69 0.31 1.2
## awkward_Self          7  0.83  0.16  0.16  0.08 0.62 0.38 1.2
## trendy_Self          59 -0.76  0.06  0.33 -0.01 0.72 0.28 1.4
## confident_Self       13 -0.76  0.21  0.21  0.01 0.76 0.24 1.3
## loner_Self           36  0.74 -0.05  0.08 -0.12 0.64 0.36 1.1
## popular_Self         45 -0.69  0.24  0.30  0.06 0.74 0.26 1.7
## plain_Self           43  0.66  0.09  0.06 -0.05 0.42 0.58 1.1
## shy_Self             52  0.62  0.19  0.05 -0.28 0.51 0.49 1.6
## social_Self          55 -0.60  0.25  0.21  0.27 0.72 0.28 2.1
## boring _Self          8  0.57 -0.05  0.27 -0.19 0.48 0.52 1.7
## outgoing_Self        41 -0.56  0.17  0.23  0.14 0.52 0.48 1.7
## flirty_Self          22 -0.55  0.06  0.24  0.21 0.51 0.49 1.7
## admired_Self          1 -0.55  0.27  0.34  0.17 0.65 0.35 2.4
## cool_Self            16 -0.54  0.29  0.41  0.12 0.68 0.32 2.6
## leader_Self          34 -0.54  0.13  0.34  0.07 0.49 0.51 1.9
## ugly_Self            61  0.53 -0.20  0.19 -0.14 0.48 0.52 1.7
## pushover_Self        46  0.52  0.04  0.24 -0.14 0.35 0.65 1.6
## poor_Self            44  0.50 -0.22  0.26  0.08 0.46 0.54 2.0
## attractive_Self       6 -0.50  0.36  0.15  0.26 0.64 0.36 2.6
## funny_Self           24 -0.37  0.33  0.06  0.28 0.45 0.55 2.9
## athletic_Self         5 -0.28  0.20  0.10  0.07 0.17 0.83 2.2
## nice_Self            40  0.09  0.85 -0.16  0.06 0.74 0.26 1.1
## considerate_Self     14  0.18  0.84 -0.15  0.03 0.70 0.30 1.2
## helpful_Self         28  0.00  0.81 -0.06  0.15 0.69 0.31 1.1
## caring_Self          11  0.04  0.77 -0.10  0.14 0.62 0.38 1.1
## genuine_Self         25 -0.01  0.76  0.02 -0.14 0.59 0.41 1.1
## loyal_Self           37  0.09  0.73  0.02 -0.11 0.51 0.49 1.1
## trustworthy_Self     60 -0.05  0.73 -0.09  0.10 0.60 0.40 1.1
## friendly_Self        23 -0.11  0.72 -0.03  0.01 0.59 0.41 1.0
## giving_Self          26 -0.03  0.71  0.02  0.00 0.52 0.48 1.0
## sympathetic_Self     58  0.00  0.71 -0.05 -0.04 0.52 0.48 1.0
## welcoming_Self       62 -0.08  0.69 -0.18  0.05 0.59 0.41 1.2
## fair_Self            20 -0.08  0.59 -0.18 -0.08 0.46 0.54 1.3
## humble_Self          30  0.21  0.55 -0.18 -0.13 0.38 0.62 1.7
## respectful_Self      47 -0.17  0.55  0.13 -0.44 0.51 0.49 2.3
## calm_Self            10 -0.22  0.54 -0.07 -0.19 0.46 0.54 1.6
## honest_Self          29 -0.24  0.49 -0.09 -0.11 0.40 0.60 1.6
## smart_Self           53  0.01  0.46 -0.12  0.09 0.24 0.76 1.2
## motivated_Self       39 -0.25  0.44  0.09 -0.25 0.35 0.65 2.3
## studious_Self        57 -0.03  0.44  0.09 -0.34 0.30 0.70 2.0
## comforting_Self      12 -0.34  0.44  0.03 -0.01 0.40 0.60 1.9
## patient_Self         42 -0.18  0.42 -0.22 -0.12 0.36 0.64 2.1
## mean_Self            38 -0.02 -0.32  0.75 -0.04 0.72 0.28 1.4
## controlling_Self     15 -0.19  0.01  0.74  0.07 0.63 0.37 1.2
## snobby_Self          54  0.01 -0.28  0.73  0.05 0.70 0.30 1.3
## rude_Self            49 -0.03 -0.25  0.72  0.02 0.65 0.35 1.2
## bossy_Self            9 -0.17 -0.12  0.70  0.13 0.62 0.38 1.3
## angry_Self            4  0.38 -0.08  0.65  0.12 0.64 0.36 1.7
## grumpy_Self          27  0.46 -0.04  0.62  0.05 0.62 0.38 1.9
## agressive_Self        3 -0.05 -0.23  0.61  0.17 0.55 0.45 1.5
## selfish_Self         51  0.17 -0.26  0.54  0.17 0.52 0.48 1.9
## jealous_Self         32  0.42  0.02  0.52  0.04 0.44 0.56 1.9
## lazy_Self            33  0.17 -0.16  0.48  0.03 0.33 0.67 1.5
## fake_Self            21  0.16 -0.40  0.47  0.05 0.51 0.49 2.2
## dependent_Self       18  0.22  0.16  0.45 -0.17 0.23 0.77 2.1
## stubborn_Self        56  0.16  0.14  0.37  0.22 0.22 0.78 2.4
## daring_Self          17 -0.15  0.15  0.13  0.67 0.62 0.38 1.3
## risky_Self           48  0.05  0.02  0.22  0.63 0.50 0.50 1.2
## rule-follower_Self   50 -0.02  0.44  0.20 -0.59 0.49 0.51 2.1
## adventurous_Self      2 -0.31  0.34  0.17  0.45 0.60 0.40 3.0
## 
##                         PA3   PA1  PA2  PA4
## SS loadings           11.60 11.35 7.23 3.18
## Proportion Var         0.19  0.18 0.12 0.05
## Cumulative Var         0.19  0.37 0.49 0.54
## Proportion Explained   0.35  0.34 0.22 0.10
## Cumulative Proportion  0.35  0.69 0.90 1.00
## 
##  With factor correlations of 
##       PA3   PA1   PA2   PA4
## PA3  1.00 -0.32 -0.01 -0.24
## PA1 -0.32  1.00 -0.17 -0.01
## PA2 -0.01 -0.17  1.00  0.27
## PA4 -0.24 -0.01  0.27  1.00
## 
## Mean item complexity =  1.6
## Test of the hypothesis that 4 factors are sufficient.
## 
## The degrees of freedom for the null model are  1891  and the objective function was  72.05 with Chi Square of  5583.84
## The degrees of freedom for the model are 1649  and the objective function was  32.32 
## 
## The root mean square of the residuals (RMSR) is  0.05 
## The df corrected root mean square of the residuals is  0.06 
## 
## The harmonic number of observations is  99 with the empirical chi square  1098.85  with prob <  1 
## The total number of observations was  100  with MLE Chi Square =  2418.93  with prob <  3e-32 
## 
## Tucker Lewis Index of factoring reliability =  0.748
## RMSEA index =  0.097  and the 90 % confidence intervals are  0.062 0.074
## BIC =  -5175
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy             
##                                                 PA3  PA1  PA2  PA4
## Correlation of scores with factors             0.99 0.98 0.98 0.93
## Multiple R square of scores with factors       0.98 0.97 0.96 0.87
## Minimum correlation of possible factor scores  0.96 0.93 0.91 0.73

We can look at how these factors group together too…

## Factor Analysis using method =  pa
## Call: fa(r = selfRateFA$Phi, nfactors = 2, rotate = "oblimin", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##     PA1   PA2   h2   u2 com
## 1  0.61 -0.19 0.44 0.56 1.2
## 2 -0.58 -0.19 0.36 0.64 1.2
## 3  0.19  0.51 0.27 0.73 1.3
## 4 -0.14  0.59 0.38 0.62 1.1
## 
##                        PA1  PA2
## SS loadings           0.77 0.68
## Proportion Var        0.19 0.17
## Cumulative Var        0.19 0.36
## Proportion Explained  0.53 0.47
## Cumulative Proportion 0.53 1.00
## 
##  With factor correlations of 
##      PA1  PA2
## PA1  1.0 -0.1
## PA2 -0.1  1.0
## 
## Mean item complexity =  1.2
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  6  and the objective function was  0.28
## The degrees of freedom for the model are -1  and the objective function was  0 
## 
## The root mean square of the residuals (RMSR) is  0 
## The df corrected root mean square of the residuals is  NA 
## 
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy             
##                                                 PA1  PA2
## Correlation of scores with factors             0.75 0.72
## Multiple R square of scores with factors       0.56 0.51
## Minimum correlation of possible factor scores  0.13 0.02

The four factors are pretty interpretable, if you ask me.

1. First (PA3), is surgency/dynamism/extraversion (reverse coded ’cause EFA): not depressed, lonely, or insecure; trendy, confident, popular, social.
2. Second (PA1), we have prosociality: caring, fair, helpful, loyal (guidelines for a model girl scout, basically).
3. Third (PA2), we have…aggression? Rude, mean, bossy, snobby, as well as lazy and fake.
4. Finally, fourth (PA4), daring, risky, adventurous, and not rule following.

Here’s nice table:

item	PA3	PA1	PA2	PA4	comm
depressed_Self	0.91	0.11	0.16	0.16	0.758
insecure_Self	0.89		0.10		0.745
lonely_Self	0.83	0.13	0.23		0.692
awkward_Self	0.83	0.16	0.16		0.620
trendy_Self	-0.76		0.33		0.715
confident_Self	-0.76	0.21	0.21		0.762
loner_Self	0.74			-0.12	0.642
popular_Self	-0.69	0.24	0.30		0.743
plain_Self	0.66				0.424
shy_Self	0.62	0.19		-0.28	0.506
social_Self	-0.60	0.25	0.21	0.27	0.720
boring _Self	0.57		0.27	-0.19	0.479
outgoing_Self	-0.56	0.17	0.23	0.14	0.517
flirty_Self	-0.55		0.24	0.21	0.508
admired_Self	-0.55	0.27	0.34	0.17	0.653
cool_Self	-0.54	0.29	0.41	0.12	0.680
leader_Self	-0.54	0.13	0.34		0.495
ugly_Self	0.53	-0.20	0.19	-0.14	0.479
pushover_Self	0.52		0.24	-0.14	0.352
poor_Self	0.50	-0.22	0.26		0.459
attractive_Self	-0.50	0.36	0.15	0.26	0.641
funny_Self	-0.37	0.33		0.28	0.454
athletic_Self	-0.28	0.20			0.171
nice_Self		0.85	-0.16		0.743
considerate_Self	0.18	0.84	-0.15		0.699
helpful_Self		0.81		0.15	0.689
caring_Self		0.77		0.14	0.625
genuine_Self		0.76		-0.14	0.590
loyal_Self		0.73		-0.11	0.514
trustworthy_Self		0.73		0.10	0.597
friendly_Self	-0.11	0.72			0.591
giving_Self		0.71			0.516
sympathetic_Self		0.71			0.520
welcoming_Self		0.69	-0.18		0.590
fair_Self		0.59	-0.18		0.456
humble_Self	0.21	0.55	-0.18	-0.13	0.382
respectful_Self	-0.17	0.55	0.13	-0.44	0.508
calm_Self	-0.22	0.54		-0.19	0.460
honest_Self	-0.24	0.49		-0.11	0.403
smart_Self		0.46	-0.12		0.243
motivated_Self	-0.25	0.44		-0.25	0.348
studious_Self		0.44		-0.34	0.296
comforting_Self	-0.34	0.44			0.397
patient_Self	-0.18	0.42	-0.22	-0.12	0.362
mean_Self		-0.32	0.75		0.722
controlling_Self	-0.19		0.74		0.631
snobby_Self		-0.28	0.73		0.701
rude_Self		-0.25	0.72		0.650
bossy_Self	-0.17	-0.12	0.70	0.13	0.623
angry_Self	0.38		0.65	0.12	0.640
grumpy_Self	0.46		0.62		0.623
agressive_Self		-0.23	0.61	0.17	0.553
selfish_Self	0.17	-0.26	0.54	0.17	0.522
jealous_Self	0.42		0.52		0.439
lazy_Self	0.17	-0.16	0.48		0.331
fake_Self	0.16	-0.40	0.47		0.515
dependent_Self	0.22	0.16	0.45	-0.17	0.235
stubborn_Self	0.16	0.14	0.37	0.22	0.224
daring_Self	-0.15	0.15	0.13	0.67	0.616
risky_Self			0.22	0.63	0.503
rule-follower_Self		0.44	0.20	-0.59	0.492
adventurous_Self	-0.31	0.34	0.17	0.45	0.596

I think this plot is supposed to show how much separation we get.

Some modifications

We realized that we can drop the risk-taking items, and maybe drop some items that are the most skewed. Let’s do that and see what happens

## Factor Analysis using method =  pa
## Call: fa(r = select(selfRateDat_lim, -matches("SelfPop")), nfactors = 2, 
##     rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                    item   PA1   PA2    h2   u2 com
## confident_Self       13  0.85 -0.06 0.741 0.26 1.0
## popular_Self         38  0.85  0.03 0.725 0.28 1.0
## social_Self          45  0.85  0.05 0.716 0.28 1.0
## trendy_Self          48  0.83  0.13 0.680 0.32 1.0
## cool_Self            16  0.80  0.13 0.641 0.36 1.1
## admired_Self          1  0.80  0.11 0.632 0.37 1.0
## attractive_Self       6  0.76 -0.05 0.593 0.41 1.0
## loner_Self           33 -0.74  0.14 0.586 0.41 1.1
## insecure_Self        28 -0.73  0.19 0.587 0.41 1.1
## outgoing_Self        34  0.72  0.08 0.518 0.48 1.0
## flirty_Self          20  0.71  0.18 0.514 0.49 1.1
## leader_Self          31  0.69  0.15 0.484 0.52 1.1
## adventurous_Self      2  0.69  0.08 0.473 0.53 1.0
## lonely_Self          32 -0.66  0.22 0.505 0.49 1.2
## depressed_Self       19 -0.66  0.28 0.541 0.46 1.4
## funny_Self           21  0.62 -0.09 0.407 0.59 1.0
## shy_Self             43 -0.62 -0.12 0.388 0.61 1.1
## awkward_Self          7 -0.60  0.22 0.428 0.57 1.3
## plain_Self           36 -0.57  0.08 0.338 0.66 1.0
## daring_Self          17  0.56  0.27 0.365 0.64 1.4
## boring _Self          8 -0.55  0.26 0.395 0.61 1.4
## comforting_Self      12  0.49 -0.31 0.361 0.64 1.7
## pushover_Self        39 -0.45  0.21 0.267 0.73 1.4
## athletic_Self         5  0.40 -0.07 0.172 0.83 1.1
## snobby_Self          44  0.12  0.79 0.627 0.37 1.0
## agressive_Self        3  0.22  0.73 0.551 0.45 1.2
## selfish_Self         42 -0.03  0.71 0.512 0.49 1.0
## bossy_Self            9  0.38  0.71 0.605 0.39 1.5
## angry_Self            4 -0.13  0.70 0.529 0.47 1.1
## grumpy_Self          24 -0.23  0.66 0.513 0.49 1.2
## controlling_Self     15  0.43  0.64 0.553 0.45 1.8
## considerate_Self     14  0.15 -0.57 0.361 0.64 1.1
## patient_Self         35  0.21 -0.56 0.376 0.62 1.3
## lazy_Self            30 -0.06  0.53 0.286 0.71 1.0
## humble_Self          27 -0.08 -0.53 0.275 0.73 1.0
## jealous_Self         29 -0.21  0.52 0.327 0.67 1.3
## calm_Self            10  0.31 -0.50 0.375 0.63 1.7
## genuine_Self         22  0.25 -0.48 0.318 0.68 1.5
## helpful_Self         25  0.38 -0.48 0.404 0.60 1.9
## poor_Self            37 -0.43  0.47 0.445 0.55 2.0
## caring_Self          11  0.32 -0.47 0.344 0.66 1.8
## honest_Self          26  0.35 -0.45 0.350 0.65 1.9
## risky_Self           40  0.34  0.45 0.292 0.71 1.9
## giving_Self          23  0.31 -0.42 0.294 0.71 1.8
## stubborn_Self        46  0.12  0.38 0.152 0.85 1.2
## rule-follower_Self   41 -0.03 -0.34 0.118 0.88 1.0
## studious_Self        47  0.06 -0.32 0.113 0.89 1.1
## dependent_Self       18 -0.09  0.23 0.065 0.94 1.3
## 
##                         PA1  PA2
## SS loadings           12.95 7.89
## Proportion Var         0.27 0.16
## Cumulative Var         0.27 0.43
## Proportion Explained   0.62 0.38
## Cumulative Proportion  0.62 1.00
## 
##  With factor correlations of 
##       PA1   PA2
## PA1  1.00 -0.09
## PA2 -0.09  1.00
## 
## Mean item complexity =  1.3
## Test of the hypothesis that 2 factors are sufficient.
## 
## The degrees of freedom for the null model are  1128  and the objective function was  46.46 with Chi Square of  3817.36
## The degrees of freedom for the model are 1033  and the objective function was  23.05 
## 
## The root mean square of the residuals (RMSR) is  0.09 
## The df corrected root mean square of the residuals is  0.1 
## 
## The harmonic number of observations is  99 with the empirical chi square  1971.92  with prob <  2.7e-61 
## The total number of observations was  100  with MLE Chi Square =  1862.85  with prob <  2.5e-50 
## 
## Tucker Lewis Index of factoring reliability =  0.655
## RMSEA index =  0.11  and the 90 % confidence intervals are  0.083 0.096
## BIC =  -2894.29
## Fit based upon off diagonal values = 0.92
## Measures of factor score adequacy             
##                                                 PA1  PA2
## Correlation of scores with factors             0.99 0.97
## Multiple R square of scores with factors       0.97 0.94
## Minimum correlation of possible factor scores  0.94 0.88

## Factor Analysis using method =  pa
## Call: fa(r = select(selfRateDat_lim, -matches("SelfPop")), nfactors = 4, 
##     rotate = "oblimin", scores = "tenBerge", fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                    item   PA1   PA3   PA2   PA4   h2   u2 com
## insecure_Self        28  0.91  0.08  0.07  0.07 0.76 0.24 1.0
## depressed_Self       19  0.90  0.07  0.13  0.14 0.74 0.26 1.1
## lonely_Self          32  0.83  0.11  0.20 -0.03 0.69 0.31 1.2
## awkward_Self          7  0.81  0.13  0.16  0.05 0.62 0.38 1.1
## confident_Self       13 -0.76  0.21  0.22  0.02 0.77 0.23 1.3
## trendy_Self          48 -0.75  0.05  0.33  0.03 0.72 0.28 1.4
## loner_Self           33  0.74 -0.04  0.06 -0.12 0.64 0.36 1.1
## popular_Self         38 -0.67  0.23  0.27  0.11 0.74 0.26 1.7
## plain_Self           36  0.64  0.11  0.11 -0.11 0.44 0.56 1.2
## shy_Self             43  0.61  0.22  0.05 -0.30 0.52 0.48 1.8
## social_Self          45 -0.59  0.22  0.19  0.27 0.72 0.28 2.0
## outgoing_Self        34 -0.55  0.14  0.22  0.16 0.52 0.48 1.7
## boring _Self          8  0.54 -0.05  0.28 -0.22 0.48 0.52 1.9
## flirty_Self          20 -0.53  0.04  0.22  0.24 0.51 0.49 1.8
## cool_Self            16 -0.52  0.31  0.41  0.12 0.70 0.30 2.7
## admired_Self          1 -0.52  0.28  0.34  0.18 0.66 0.34 2.6
## leader_Self          31 -0.51  0.15  0.34  0.09 0.50 0.50 2.0
## poor_Self            37  0.51 -0.24  0.24  0.10 0.46 0.54 2.0
## pushover_Self        39  0.50  0.02  0.25 -0.15 0.35 0.65 1.7
## attractive_Self       6 -0.46  0.34  0.10  0.31 0.63 0.37 2.8
## funny_Self           21 -0.35  0.30  0.00  0.32 0.45 0.55 3.0
## athletic_Self         5 -0.25  0.23  0.09  0.08 0.18 0.82 2.5
## helpful_Self         25  0.02  0.84 -0.08  0.15 0.75 0.25 1.1
## considerate_Self     14  0.17  0.83 -0.16  0.02 0.69 0.31 1.2
## caring_Self          11  0.04  0.75 -0.13  0.15 0.61 0.39 1.2
## genuine_Self         22 -0.01  0.75  0.00 -0.11 0.57 0.43 1.0
## giving_Self          23 -0.01  0.70 -0.05  0.06 0.50 0.50 1.0
## humble_Self          27  0.21  0.61 -0.18 -0.13 0.43 0.57 1.5
## calm_Self            10 -0.25  0.57 -0.01 -0.26 0.50 0.50 1.8
## honest_Self          26 -0.24  0.48 -0.12 -0.05 0.39 0.61 1.6
## patient_Self         35 -0.21  0.48 -0.18 -0.19 0.41 0.59 2.0
## comforting_Self      12 -0.32  0.45 -0.02  0.04 0.40 0.60 1.8
## studious_Self        47 -0.03  0.42  0.07 -0.28 0.24 0.76 1.8
## controlling_Self     15 -0.19 -0.03  0.76  0.06 0.66 0.34 1.1
## snobby_Self          44  0.00 -0.28  0.75  0.01 0.69 0.31 1.3
## bossy_Self            9 -0.14 -0.15  0.68  0.17 0.63 0.37 1.3
## agressive_Self        3 -0.06 -0.25  0.63  0.12 0.56 0.44 1.4
## angry_Self            4  0.39 -0.12  0.61  0.13 0.63 0.37 1.9
## grumpy_Self          24  0.47 -0.09  0.60  0.08 0.64 0.36 2.0
## jealous_Self         29  0.39 -0.05  0.50  0.01 0.43 0.57 1.9
## lazy_Self            30  0.16 -0.15  0.50 -0.03 0.33 0.67 1.4
## selfish_Self         42  0.20 -0.30  0.49  0.20 0.51 0.49 2.5
## dependent_Self       18  0.20  0.15  0.45 -0.19 0.23 0.77 2.0
## stubborn_Self        46  0.19  0.08  0.34  0.26 0.24 0.76 2.6
## daring_Self          17 -0.10  0.11  0.04  0.72 0.63 0.37 1.1
## risky_Self           40  0.11 -0.01  0.16  0.68 0.53 0.47 1.2
## rule-follower_Self   41 -0.05  0.45  0.21 -0.57 0.45 0.55 2.2
## adventurous_Self      2 -0.27  0.31  0.11  0.49 0.60 0.40 2.5
## 
##                         PA1  PA3  PA2  PA4
## SS loadings           10.78 6.48 5.46 3.31
## Proportion Var         0.22 0.14 0.11 0.07
## Cumulative Var         0.22 0.36 0.47 0.54
## Proportion Explained   0.41 0.25 0.21 0.13
## Cumulative Proportion  0.41 0.66 0.87 1.00
## 
##  With factor correlations of 
##       PA1   PA3   PA2   PA4
## PA1  1.00 -0.31 -0.01 -0.30
## PA3 -0.31  1.00 -0.10  0.04
## PA2 -0.01 -0.10  1.00  0.34
## PA4 -0.30  0.04  0.34  1.00
## 
## Mean item complexity =  1.7
## Test of the hypothesis that 4 factors are sufficient.
## 
## The degrees of freedom for the null model are  1128  and the objective function was  46.46 with Chi Square of  3817.36
## The degrees of freedom for the model are 942  and the objective function was  16.73 
## 
## The root mean square of the residuals (RMSR) is  0.05 
## The df corrected root mean square of the residuals is  0.06 
## 
## The harmonic number of observations is  99 with the empirical chi square  573.57  with prob <  1 
## The total number of observations was  100  with MLE Chi Square =  1329.86  with prob <  9e-16 
## 
## Tucker Lewis Index of factoring reliability =  0.819
## RMSEA index =  0.088  and the 90 % confidence intervals are  0.056 0.072
## BIC =  -3008.22
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy             
##                                                 PA1  PA3  PA2  PA4
## Correlation of scores with factors             0.98 0.97 0.97 0.93
## Multiple R square of scores with factors       0.97 0.94 0.94 0.86
## Minimum correlation of possible factor scores  0.94 0.88 0.87 0.73

These clusters of items may still be related to status (and they’re actually pretty close to the expected factors, just divided up a bit more). We can correlate self rated accepted and controversial status with the factor scores to start exploring this.

Correlations

In the output below, SelfPop_1 is controversial, and SelfPop_2 is accepted.

Also:

1. Surgency/dynamism (PA3)
2. Prosociality (PA1)
3. Aggression (PA2)
4. Daring (PA4)

We see that controversial status is correlated with aggression and with risk-taking.

We see accepted status is highly correlated with the surgency/dynamism component (remember, reverse the sign here because of the depression item anchoring the scale).

## Call:corr.test(x = as.data.frame(selfPopDat), y = as.data.frame(predict(selfRateFA, 
##     selfRateDat_nopop_imputed, missing = T, use = "pairwise.complete.obs")), 
##     use = "pairwise.complete.obs", adjust = "none")
## Correlation matrix 
##              V1    V2   V3   V4
## SelfPop_1  0.05 -0.18 0.52 0.22
## SelfPop_2 -0.71  0.16 0.14 0.10
## Sample Size 
##            V1  V2  V3  V4
## SelfPop_1  98  98  98  98
## SelfPop_2 100 100 100 100
##            V1   V2   V3   V4
## SelfPop_1 0.6 0.08 0.00 0.03
## SelfPop_2 0.0 0.12 0.17 0.33
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

Grain of salt: No correction for multiple comparison here.

Slightly bigger grain of salt: 8 folks are missing a rating on a couple items here and there, so I impute the mean so we can get predicted factor scores. This means that significance values and CIs close to threshold below should be treated lightly (but it doesn’t change things too much).

This gets more interesting in the regressions.

Regressing Controversial Status

Here’s the raw output for regressing controversial status on the component scores – see below for a table with CIs.

## 
## Call: rlm(formula = selfPopDat[, c("SelfPop_1")] ~ predict(selfRateFA, 
##     selfRateDat_nopop_imputed))
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.02969 -0.63801 -0.06832  0.71037  3.75564 
## 
## Coefficients:
##                                                 Value   Std. Error t value
## (Intercept)                                      2.3128  0.1243    18.6025
## predict(selfRateFA, selfRateDat_nopop_imputed)1  0.0440  0.1248     0.3527
## predict(selfRateFA, selfRateDat_nopop_imputed)2 -0.3489  0.1248    -2.7956
## predict(selfRateFA, selfRateDat_nopop_imputed)3  0.9388  0.1246     7.5343
## predict(selfRateFA, selfRateDat_nopop_imputed)4  0.2658  0.1250     2.1259
## 
## Residual standard error: 0.977 on 93 degrees of freedom
##   (2 observations deleted due to missingness)

Results from bootstrap estimates: Controversial status is significantly predicted by lower prosocial scores (2), and higher aggression scores (3). Estimates for risk-taking (4) is positive and just past threshold.

Controversial status relation with component scores, bootstrapped CIs

component	est	lower 95%	upper 95%
1	0.04	-0.18	0.31
2	-0.35	-0.67	-0.09
3	0.94	0.61	1.23
4	0.27	0.01	0.70

Regressing Accepted Status

Here’s the raw output for an rlm of accepted status on the component scores. Again, scroll down for a nice table.

## 
## Call: rlm(formula = selfPopDat[, c("SelfPop_2")] ~ predict(selfRateFA, 
##     selfRateDat_nopop_imputed))
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -3.457979 -0.571774  0.003142  0.579391  2.649151 
## 
## Coefficients:
##                                                 Value    Std. Error
## (Intercept)                                       3.5265   0.1042  
## predict(selfRateFA, selfRateDat_nopop_imputed)1  -1.2461   0.1048  
## predict(selfRateFA, selfRateDat_nopop_imputed)2   0.2824   0.1048  
## predict(selfRateFA, selfRateDat_nopop_imputed)3   0.3293   0.1048  
## predict(selfRateFA, selfRateDat_nopop_imputed)4   0.1719   0.1047  
##                                                 t value 
## (Intercept)                                      33.8405
## predict(selfRateFA, selfRateDat_nopop_imputed)1 -11.8864
## predict(selfRateFA, selfRateDat_nopop_imputed)2   2.6959
## predict(selfRateFA, selfRateDat_nopop_imputed)3   3.1418
## predict(selfRateFA, selfRateDat_nopop_imputed)4   1.6424
## 
## Residual standard error: 0.8548 on 95 degrees of freedom

Accepted status is significantly predicted by higher surgency (1; remember, flip the sign), and prosocial scores (2). Interestingly aggression (3) is also significant.

Accepted status relation with component scores, bootstrapped CIs

component	est	lower 95%	upper 95%
1	-1.25	-1.44	-1.00
2	0.28	0.08	0.49
3	0.33	0.06	0.57
4	0.17	-0.11	0.42

What has EFA told us?

Well, we have four factors that are helpfully related to self reported status. This is what we want. All four factors seem relevant.

EFA using machine learning to select items

Now we need a principled way to select items. We could use some communality cutoff, or loading strength. But we know we want 48 items, so let’s start there. We can use regularized regression methods to let the machine learn what 48 items give us the best set of factors. We can then compare that to the EFA results as well as to the earlier classification.

## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 30
## iterations 10
## iterations 20
## iterations 10
## iterations 20
## iterations 30

## [[1]]
##   para Nitems 
##      1     44 
## 
## [[2]]
##   para Nitems 
##    1.2   44.0 
## 
## [[3]]
##   para Nitems 
##    1.4   43.0 
## 
## [[4]]
##   para Nitems 
##    1.6   40.0 
## 
## [[5]]
##   para Nitems 
##    1.8   36.0 
## 
## [[6]]
##   para Nitems 
##      2     32

A penalty parameter of 1.4 (#3) gives us the number of items we want (48 unique).

	PC1	PC2	PC3	PC4
admired_Self	-0.092
adventurous_Self				0.248
agressive_Self		0.176
angry_Self		0.395
athletic_Self
attractive_Self	-0.178
awkward_Self	0.287
boring _Self	0.045
bossy_Self		0.498
calm_Self			0.195
caring_Self
comforting_Self			0.022
confident_Self	-0.346
considerate_Self			0.335
controlling_Self		0.394
cool_Self	-0.123
daring_Self				0.78
dependent_Self
depressed_Self	0.3
flirty_Self	-0.003
funny_Self
genuine_Self			0.362
giving_Self			0.435
grumpy_Self		0.308
helpful_Self			0.637
honest_Self
humble_Self			0.176
insecure_Self	0.439
jealous_Self		0.105
lazy_Self		0.071
leader_Self	-0.096
lonely_Self	0.221
loner_Self	0.35
outgoing_Self	-0.141
patient_Self			0.1
plain_Self	0.047
poor_Self	0.025
popular_Self	-0.328
pushover_Self	0.031
risky_Self				0.574
rule-follower_Self			0.266
selfish_Self		0.065
shy_Self	0.165
snobby_Self		0.541
social_Self	-0.317
stubborn_Self		0.049
studious_Self			0.111
trendy_Self	-0.137

The next obvious step is to look and see what a regular EFA tells us about this selection of items

Whammo, 4 factors again.

## Factor Analysis using method =  pa
## Call: fa(r = eItemDF, nfactors = 4, rotate = "oblimin", scores = "tenBerge", 
##     fm = "pa", use = "pairwise.complete.obs")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                    item   PA1   PA3   PA2   PA4   h2   u2 com
## depressed_Self       16  0.90  0.04  0.08  0.16 0.74 0.26 1.1
## insecure_Self        23  0.90  0.06  0.06  0.03 0.76 0.24 1.0
## lonely_Self          27  0.84  0.11  0.17 -0.04 0.70 0.30 1.1
## awkward_Self          6  0.82  0.13  0.14  0.05 0.62 0.38 1.1
## loner_Self           28  0.74 -0.05  0.04 -0.14 0.65 0.35 1.1
## trendy_Self          43 -0.73  0.07  0.36  0.01 0.72 0.28 1.5
## confident_Self       11 -0.71  0.24  0.23  0.06 0.77 0.23 1.5
## plain_Self           31  0.65  0.13  0.09 -0.12 0.45 0.55 1.2
## popular_Self         33 -0.63  0.25  0.28  0.14 0.74 0.26 1.9
## shy_Self             38  0.62  0.21 -0.02 -0.24 0.50 0.50 1.5
## boring _Self          7  0.59 -0.01  0.23 -0.16 0.45 0.55 1.5
## social_Self          40 -0.57  0.21  0.20  0.29 0.72 0.28 2.1
## pushover_Self        34  0.53  0.04  0.22 -0.13 0.35 0.65 1.5
## poor_Self            32  0.53 -0.25  0.23  0.09 0.47 0.53 1.9
## flirty_Self          17 -0.51  0.01  0.21  0.28 0.52 0.48 1.9
## outgoing_Self        29 -0.51  0.15  0.21  0.21 0.52 0.48 1.9
## leader_Self          26 -0.48  0.18  0.38  0.08 0.51 0.49 2.3
## cool_Self            14 -0.47  0.34  0.40  0.18 0.71 0.29 3.1
## admired_Self          1 -0.47  0.30  0.34  0.21 0.67 0.33 3.1
## attractive_Self       5 -0.43  0.32  0.11  0.33 0.62 0.38 2.9
## considerate_Self     12  0.17  0.80 -0.21  0.08 0.66 0.34 1.3
## helpful_Self         21  0.04  0.79 -0.14  0.23 0.71 0.29 1.2
## genuine_Self         18  0.00  0.74 -0.02 -0.07 0.55 0.45 1.0
## giving_Self          19  0.01  0.67 -0.10  0.13 0.49 0.51 1.1
## calm_Self             9 -0.22  0.63 -0.01 -0.22 0.52 0.48 1.5
## humble_Self          22  0.22  0.61 -0.20 -0.10 0.43 0.57 1.6
## patient_Self         30 -0.17  0.50 -0.24 -0.08 0.42 0.58 1.8
## studious_Self        42 -0.02  0.46  0.06 -0.27 0.25 0.75 1.7
## comforting_Self      10 -0.29  0.45 -0.03  0.09 0.41 0.59 1.8
## controlling_Self     13 -0.16 -0.01  0.79  0.02 0.67 0.33 1.1
## bossy_Self            8 -0.11 -0.13  0.72  0.12 0.64 0.36 1.2
## snobby_Self          39  0.07 -0.24  0.72  0.06 0.65 0.35 1.3
## agressive_Self        3 -0.03 -0.23  0.66  0.09 0.57 0.43 1.3
## angry_Self            4  0.40 -0.12  0.62  0.09 0.63 0.37 1.9
## grumpy_Self          20  0.49 -0.08  0.61  0.03 0.64 0.36 2.0
## selfish_Self         37  0.20 -0.32  0.49  0.16 0.51 0.49 2.3
## lazy_Self            25  0.19 -0.14  0.48 -0.01 0.32 0.68 1.5
## jealous_Self         24  0.43 -0.04  0.47  0.03 0.41 0.59 2.0
## stubborn_Self        41  0.19  0.09  0.38  0.20 0.24 0.76 2.2
## daring_Self          15 -0.06  0.05 -0.01  0.82 0.71 0.29 1.0
## risky_Self           35  0.12 -0.07  0.17  0.67 0.52 0.48 1.2
## adventurous_Self      2 -0.23  0.28  0.08  0.56 0.62 0.38 1.9
## rule-follower_Self   36 -0.02  0.53  0.20 -0.53 0.45 0.55 2.3
## 
##                         PA1  PA3  PA2  PA4
## SS loadings           10.11 5.43 5.37 3.27
## Proportion Var         0.24 0.13 0.12 0.08
## Cumulative Var         0.24 0.36 0.49 0.56
## Proportion Explained   0.42 0.22 0.22 0.14
## Cumulative Proportion  0.42 0.64 0.86 1.00
## 
##  With factor correlations of 
##       PA1   PA3   PA2   PA4
## PA1  1.00 -0.31 -0.02 -0.31
## PA3 -0.31  1.00 -0.11  0.09
## PA2 -0.02 -0.11  1.00  0.35
## PA4 -0.31  0.09  0.35  1.00
## 
## Mean item complexity =  1.7
## Test of the hypothesis that 4 factors are sufficient.
## 
## The degrees of freedom for the null model are  903  and the objective function was  40.07 with Chi Square of  3359.29
## The degrees of freedom for the model are 737  and the objective function was  12.6 
## 
## The root mean square of the residuals (RMSR) is  0.05 
## The df corrected root mean square of the residuals is  0.05 
## 
## The harmonic number of observations is  99 with the empirical chi square  422.8  with prob <  1 
## The total number of observations was  100  with MLE Chi Square =  1022.96  with prob <  1.2e-11 
## 
## Tucker Lewis Index of factoring reliability =  0.851
## RMSEA index =  0.084  and the 90 % confidence intervals are  0.053 0.071
## BIC =  -2371.05
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy             
##                                                 PA1  PA3  PA2  PA4
## Correlation of scores with factors             0.98 0.96 0.97 0.93
## Multiple R square of scores with factors       0.97 0.92 0.93 0.87
## Minimum correlation of possible factor scores  0.93 0.85 0.87 0.75

item	PA1	PA3	PA2	PA4	comm
depressed_Self	0.90			0.16	0.74
insecure_Self	0.90				0.76
lonely_Self	0.84	0.11	0.17		0.70
awkward_Self	0.82	0.13	0.14		0.62
loner_Self	0.74			-0.14	0.65
trendy_Self	-0.73		0.36		0.72
confident_Self	-0.71	0.24	0.23		0.77
plain_Self	0.65	0.13		-0.12	0.45
popular_Self	-0.63	0.25	0.28	0.14	0.74
shy_Self	0.62	0.21		-0.24	0.50
boring _Self	0.59		0.23	-0.16	0.45
social_Self	-0.57	0.21	0.20	0.29	0.72
pushover_Self	0.53		0.22	-0.13	0.35
poor_Self	0.53	-0.25	0.23		0.47
flirty_Self	-0.51		0.21	0.28	0.52
outgoing_Self	-0.51	0.15	0.21	0.21	0.52
leader_Self	-0.48	0.18	0.38		0.51
cool_Self	-0.47	0.34	0.40	0.18	0.71
admired_Self	-0.47	0.30	0.34	0.21	0.67
attractive_Self	-0.43	0.32	0.11	0.33	0.62
considerate_Self	0.17	0.80	-0.21		0.66
helpful_Self		0.79	-0.14	0.23	0.71
genuine_Self		0.74			0.55
giving_Self		0.67	-0.10	0.13	0.49
calm_Self	-0.22	0.63		-0.22	0.52
humble_Self	0.22	0.61	-0.20	-0.10	0.43
patient_Self	-0.17	0.50	-0.24		0.42
studious_Self		0.46		-0.27	0.25
comforting_Self	-0.29	0.45			0.41
controlling_Self	-0.16		0.79		0.67
bossy_Self	-0.11	-0.13	0.72	0.12	0.64
snobby_Self		-0.24	0.72		0.65
agressive_Self		-0.23	0.66		0.57
angry_Self	0.40	-0.12	0.62		0.63
grumpy_Self	0.49		0.61		0.64
selfish_Self	0.20	-0.32	0.49	0.16	0.51
lazy_Self	0.19	-0.14	0.48		0.32
jealous_Self	0.43		0.47		0.41
stubborn_Self	0.19		0.38	0.20	0.24
daring_Self				0.82	0.71
risky_Self	0.12		0.17	0.67	0.52
adventurous_Self	-0.23	0.28		0.56	0.62
rule-follower_Self		0.53	0.20	-0.53	0.45

For reference, the original EFA with items that also appear above in bold.

Original EFA, retained items bolded

item	PA3	PA1	PA2	PA4	comm
depressed_Self	0.91	0.11	0.16	0.16	0.758
insecure_Self	0.89		0.10		0.745
lonely_Self	0.83	0.13	0.23		0.692
awkward_Self	0.83	0.16	0.16		0.620
trendy_Self	-0.76		0.33		0.715
confident_Self	-0.76	0.21	0.21		0.762
loner_Self	0.74			-0.12	0.642
popular_Self	-0.69	0.24	0.30		0.743
plain_Self	0.66				0.424
shy_Self	0.62	0.19		-0.28	0.506
social_Self	-0.60	0.25	0.21	0.27	0.720
boring_Self	0.57		0.27	-0.19	0.479
outgoing_Self	-0.56	0.17	0.23	0.14	0.517
flirty_Self	-0.55		0.24	0.21	0.508
admired_Self	-0.55	0.27	0.34	0.17	0.653
cool_Self	-0.54	0.29	0.41	0.12	0.680
leader_Self	-0.54	0.13	0.34		0.495
ugly_Self	0.53	-0.20	0.19	-0.14	0.479
pushover_Self	0.52		0.24	-0.14	0.352
poor_Self	0.50	-0.22	0.26		0.459
attractive_Self	-0.50	0.36	0.15	0.26	0.641
funny_Self	-0.37	0.33		0.28	0.454
athletic_Self	-0.28	0.20			0.171
nice_Self		0.85	-0.16		0.743
considerate_Self	0.18	0.84	-0.15		0.699
helpful_Self		0.81		0.15	0.689
caring_Self		0.77		0.14	0.625
genuine_Self		0.76		-0.14	0.590
loyal_Self		0.73		-0.11	0.514
trustworthy_Self		0.73		0.10	0.597
friendly_Self	-0.11	0.72			0.591
giving_Self		0.71			0.516
sympathetic_Self		0.71			0.520
welcoming_Self		0.69	-0.18		0.590
fair_Self		0.59	-0.18		0.456
humble_Self	0.21	0.55	-0.18	-0.13	0.382
respectful_Self	-0.17	0.55	0.13	-0.44	0.508
calm_Self	-0.22	0.54		-0.19	0.460
honest_Self	-0.24	0.49		-0.11	0.403
smart_Self		0.46	-0.12		0.243
motivated_Self	-0.25	0.44		-0.25	0.348
studious_Self		0.44		-0.34	0.296
comforting_Self	-0.34	0.44			0.397
patient_Self	-0.18	0.42	-0.22	-0.12	0.362
mean_Self		-0.32	0.75		0.722
controlling_Self	-0.19		0.74		0.631
snobby_Self		-0.28	0.73		0.701
rude_Self		-0.25	0.72		0.650
bossy_Self	-0.17	-0.12	0.70	0.13	0.623
angry_Self	0.38		0.65	0.12	0.640
grumpy_Self	0.46		0.62		0.623
agressive_Self		-0.23	0.61	0.17	0.553
selfish_Self	0.17	-0.26	0.54	0.17	0.522
jealous_Self	0.42		0.52		0.439
lazy_Self	0.17	-0.16	0.48		0.331
fake_Self	0.16	-0.40	0.47		0.515
dependent_Self	0.22	0.16	0.45	-0.17	0.235
stubborn_Self	0.16	0.14	0.37	0.22	0.224
daring_Self	-0.15	0.15	0.13	0.67	0.616
risky_Self			0.22	0.63	0.503
rule-follower_Self		0.44	0.20	-0.59	0.492
adventurous_Self	-0.31	0.34	0.17	0.45	0.596

Pick items by X-loading and Communality

We could also pick items based on cross loadings (minimizing) and communality (maximizing).

item	max	maxPA	ssXload	comm	scalemax	scalessX	scalecomm	crit
athletic_Self	-0.25	PA1	0.07	0.18	-2.33	0.41	-2.35	-1.42
funny_Self	-0.35	PA1	0.19	0.45	-1.73	-1.24	-0.59	-1.19
attractive_Self	-0.46	PA1	0.22	0.63	-1.00	-1.49	0.57	-0.64
pushover_Self	0.50	PA1	0.09	0.35	-0.69	0.10	-1.27	-0.62
leader_Self	-0.51	PA1	0.15	0.50	-0.63	-0.75	-0.26	-0.54
poor_Self	0.51	PA1	0.13	0.46	-0.64	-0.44	-0.55	-0.54
cool_Self	-0.52	PA1	0.28	0.70	-0.55	-2.02	1.05	-0.50
boring_Self	0.54	PA1	0.13	0.48	-0.43	-0.54	-0.44	-0.47
admired_Self	-0.52	PA1	0.22	0.66	-0.57	-1.52	0.80	-0.43
flirty_Self	-0.53	PA1	0.11	0.51	-0.53	-0.21	-0.20	-0.31
shy_Self	0.61	PA1	0.14	0.52	0.05	-0.65	-0.12	-0.24
outgoing_Self	-0.55	PA1	0.09	0.52	-0.39	0.00	-0.17	-0.19
social_Self	-0.59	PA1	0.16	0.72	-0.11	-0.85	1.15	0.07
plain_Self	0.64	PA1	0.04	0.44	0.24	1.05	-0.69	0.20
popular_Self	-0.67	PA1	0.14	0.74	0.40	-0.61	1.27	0.35
trendy_Self	-0.75	PA1	0.11	0.72	0.97	-0.25	1.18	0.63
confident_Self	-0.76	PA1	0.09	0.77	1.00	0.03	1.48	0.83
awkward_Self	0.81	PA1	0.05	0.62	1.37	0.86	0.50	0.91
loner_Self	0.74	PA1	0.02	0.64	0.89	1.51	0.62	1.01
lonely_Self	0.83	PA1	0.05	0.69	1.47	0.70	0.96	1.04
depressed_Self	0.90	PA1	0.04	0.74	1.91	0.96	1.32	1.39
insecure_Self	0.91	PA1	0.02	0.76	2.00	1.67	1.45	1.71
stubborn_Self	0.34	PA2	0.11	0.24	-1.79	-0.22	-1.99	-1.33
dependent_Self	0.45	PA2	0.10	0.23	-1.01	-0.08	-2.04	-1.04
jealous_Self	0.50	PA2	0.16	0.43	-0.68	-0.81	-0.77	-0.75
selfish_Self	0.49	PA2	0.17	0.51	-0.80	-0.98	-0.21	-0.66
lazy_Self	0.50	PA2	0.05	0.33	-0.68	0.78	-1.41	-0.44
grumpy_Self	0.60	PA2	0.23	0.64	-0.06	-1.65	0.62	-0.36
angry_Self	0.61	PA2	0.19	0.63	0.03	-1.15	0.54	-0.19
agressive_Self	0.63	PA2	0.08	0.56	0.18	0.18	0.15	0.17
bossy_Self	0.68	PA2	0.07	0.63	0.50	0.37	0.61	0.49
snobby_Self	0.75	PA2	0.08	0.69	0.95	0.26	0.97	0.73
controlling_Self	0.76	PA2	0.04	0.66	1.00	0.92	0.76	0.90
studious_Self	0.42	PA3	0.08	0.24	-1.22	0.15	-2.01	-1.03
comforting_Self	0.45	PA3	0.10	0.40	-1.06	-0.12	-0.94	-0.71
patient_Self	0.48	PA3	0.11	0.41	-0.83	-0.25	-0.84	-0.64
honest_Self	0.48	PA3	0.08	0.39	-0.82	0.30	-1.02	-0.51
calm_Self	0.57	PA3	0.13	0.50	-0.21	-0.51	-0.26	-0.33
humble_Self	0.61	PA3	0.09	0.43	-0.01	-0.01	-0.74	-0.25
caring_Self	0.75	PA3	0.04	0.61	0.98	0.90	0.43	0.77
giving_Self	0.70	PA3	0.01	0.50	0.58	2.09	-0.26	0.80
genuine_Self	0.75	PA3	0.01	0.57	0.94	1.79	0.20	0.98
considerate_Self	0.83	PA3	0.06	0.69	1.49	0.64	0.95	1.03
helpful_Self	0.84	PA3	0.03	0.75	1.57	1.24	1.34	1.38
rule-follower_Self	-0.57	PA4	0.25	0.45	-0.24	-1.79	-0.62	-0.88
adventurous_Self	0.49	PA4	0.19	0.60	-0.80	-1.15	0.36	-0.53
risky_Self	0.68	PA4	0.04	0.53	0.46	1.06	-0.11	0.47
daring_Self	0.72	PA4	0.03	0.63	0.77	1.35	0.56	0.89

Based on this table, we could drop items with low scores on ‘crit’, which is just an average of Z scores for each of our criteria (main factor loading, cross-loadings, and communality). I can’t think of a principled way to do this, and given the imbalance already in the number of items, we can’t really set an arbitrary number per factor.

I’m going to set this route aside for no, because the SPCA item selection seems fine for now, especially if we get good prediction below. (The basis behind SPCA is the same as PCA/EFA, which is is to identify loadings on factors that capture the maximum amount of variance in the data. In light of that, the 48 items should do what we want).

Regressions with new items

48 items: Regressing Controversial Status

## 
## Call: rlm(formula = selfPopDat[, c("SelfPop_1")] ~ predict(eItemFA, 
##     eitemDF_imputed))
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.04491 -0.65924 -0.03565  0.59240  3.71589 
## 
## Coefficients:
##                                    Value   Std. Error t value
## (Intercept)                         2.3116  0.1172    19.7302
## predict(eItemFA, eitemDF_imputed)1  0.0647  0.1177     0.5496
## predict(eItemFA, eitemDF_imputed)2 -0.3350  0.1175    -2.8496
## predict(eItemFA, eitemDF_imputed)3  0.9661  0.1175     8.2228
## predict(eItemFA, eitemDF_imputed)4  0.2297  0.1177     1.9520
## 
## Residual standard error: 0.9275 on 93 degrees of freedom
##   (2 observations deleted due to missingness)

Results from bootstrap estimates: Controversial status is significantly predicted by lower prosocial scores (2), and higher aggression scores (3). Estimates for risk-taking (4) is positive and just past threshold.

Controversial status relation with component scores, bootstrapped CIs

component	est	lower 95%	upper 95%
1	0.06	-0.17	0.34
2	-0.33	-0.64	-0.09
3	0.97	0.60	1.26
4	0.23	-0.03	0.68

48 item: Regressing Accepted Status

Here’s the raw output for an rlm of accepted status on the component scores. Again, scroll down for a nice table.

## 
## Call: rlm(formula = selfPopDat[, c("SelfPop_2")] ~ predict(eItemFA, 
##     eitemDF_imputed))
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.37900 -0.59417 -0.01366  0.65695  2.63990 
## 
## Coefficients:
##                                    Value    Std. Error t value 
## (Intercept)                          3.5236   0.1069    32.9695
## predict(eItemFA, eitemDF_imputed)1  -1.1987   0.1075   -11.1494
## predict(eItemFA, eitemDF_imputed)2   0.3376   0.1075     3.1414
## predict(eItemFA, eitemDF_imputed)3   0.3617   0.1075     3.3648
## predict(eItemFA, eitemDF_imputed)4   0.2102   0.1074     1.9573
## 
## Residual standard error: 0.9656 on 95 degrees of freedom

Accepted status is significantly predicted by higher surgency (1; remember, flip the sign), and prosocial scores (2). Interestingly aggression (3) is also significant.

Accepted status relation with component scores, bootstrapped CIs

component	est	lower 95%	upper 95%
1	-1.25	-1.44	-1.00
2	0.28	0.08	0.49
3	0.33	0.06	0.57
4	0.17	-0.11	0.42

48 items collapsed into 4 scales

Let’s see how this scale works if we just pretend we have a scale.

See raw summary, and below that, tables of bootstrapped CIs.

## 
## Call: rlm(formula = SelfPop_1 ~ 1 + admired + adventurous + agressive + 
##     calm, data = selfRateSPCAScaleScores)
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.30475 -0.72393 -0.07895  0.70616  3.48107 
## 
## Coefficients:
##             Value   Std. Error t value
## (Intercept)  1.3843  1.3414     1.0319
## admired     -0.1857  0.1332    -1.3939
## adventurous -0.0118  0.1463    -0.0809
## agressive    0.9170  0.1409     6.5073
## calm        -0.1865  0.1800    -1.0365
## 
## Residual standard error: 1.062 on 93 degrees of freedom
##   (2 observations deleted due to missingness)

## 
## Call: rlm(formula = SelfPop_2 ~ 1 + admired + adventurous + agressive + 
##     calm, data = selfRateSPCAScaleScores)
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -2.848951 -0.555426  0.004171  0.710507  2.765419 
## 
## Coefficients:
##             Value    Std. Error t value 
## (Intercept)   8.4466   1.2219     6.9128
## admired      -1.2445   0.1212   -10.2676
## adventurous  -0.3007   0.1322    -2.2746
## agressive     0.1708   0.1280     1.3343
## calm         -0.0649   0.1632    -0.3976
## 
## Residual standard error: 0.8768 on 95 degrees of freedom

## Call:corr.test(x = select(selfRateSPCAScaleScores, matches("SelfPop")), 
##     y = select(selfRateSPCAScaleScores, admired, adventurous, 
##         agressive, calm), use = "pairwise.complete.obs", adjust = "none")
## Correlation matrix 
##           admired adventurous agressive  calm
## SelfPop_1   -0.02        0.28      0.58 -0.28
## SelfPop_2   -0.72        0.20     -0.06  0.22
## Sample Size 
##           admired adventurous agressive calm
## SelfPop_1      98          98        98   98
## SelfPop_2     100         100       100  100
##           admired adventurous agressive calm
## SelfPop_1    0.82        0.01      0.00 0.01
## SelfPop_2    0.00        0.04      0.59 0.03
## 
##  To see confidence intervals of the correlations, print with the short=FALSE option

Controversial status relation with scale scores, bootstrapped CIs

	est	lower 95%	upper 95%
d[, 2:col]admired	-0.19	-0.44	0.19
d[, 2:col]adventurous	-0.01	-0.34	0.52
d[, 2:col]agressive	0.92	0.54	1.23
d[, 2:col]calm	-0.19	-0.61	0.16

Accepted status relation with scale scores, bootstrapped CIs

	est	lower 95%	upper 95%
d[, 2:col]admired	-1.24	-1.45	-0.98
d[, 2:col]adventurous	-0.30	-0.63	0.02
d[, 2:col]agressive	0.17	-0.12	0.41
d[, 2:col]calm	-0.06	-0.41	0.22

Ultimately, when we reduce the items to scale scores, only the strongest predictors survive (though note the correlations above). Aggression, all else equal, predicts Controversial High Status. Extraversion, all else equal, predicts accepted status.

A Little CFA

## admired=~admired_Self+attractive_Self+awkward_Self+boring_Self+confident_Self+cool_Self+depressed_Self+flirty_Self+insecure_Self+leader_Self+lonely_Self+loner_Self+outgoing_Self+plain_Self+poor_Self+popular_Self+pushover_Self+shy_Self+social_Self+trendy_Self
## agressive=~agressive_Self+angry_Self+bossy_Self+controlling_Self+grumpy_Self+jealous_Self+lazy_Self+selfish_Self+snobby_Self+stubborn_Self
## calm=~calm_Self+comforting_Self+considerate_Self+genuine_Self+giving_Self+helpful_Self+humble_Self+patient_Self+studious_Self
## adventurous=~adventurous_Self+daring_Self+risky_Self+rulefollower_Self

## lavaan (0.5-18) converged normally after  42 iterations
## 
##                                                   Used       Total
##   Number of observations                            95         100
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             1844.309
##   Degrees of freedom                               854
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             3903.054
##   Degrees of freedom                               903
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.670
##   Tucker-Lewis Index (TLI)                       0.651
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)              -6315.998
##   Loglikelihood unrestricted model (H1)      -5393.843
## 
##   Number of free parameters                         92
##   Akaike (AIC)                               12815.996
##   Bayesian (BIC)                             13050.952
##   Sample-size adjusted Bayesian (BIC)        12760.488
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.110
##   90 Percent Confidence Interval          0.104  0.117
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.147
## 
## Parameter estimates:
## 
##   Information                                 Expected
##   Standard Errors                             Standard
## 
##                    Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
## Latent variables:
##   admired =~
##     admired_Self      1.000                               1.122    0.755
##     attractiv_Slf     0.888    0.118    7.553    0.000    0.996    0.737
##     awkward_Self     -1.009    0.148   -6.837    0.000   -1.133   -0.675
##     boring_Self      -0.802    0.134   -5.992    0.000   -0.900   -0.599
##     confident_Slf     1.213    0.133    9.119    0.000    1.361    0.865
##     cool_Self         1.008    0.130    7.744    0.000    1.131    0.753
##     depressed_Slf    -1.114    0.147   -7.577    0.000   -1.250   -0.739
##     flirty_Self       1.004    0.143    7.034    0.000    1.127    0.692
##     insecure_Self    -1.234    0.151   -8.192    0.000   -1.385   -0.790
##     leader_Self       0.910    0.136    6.673    0.000    1.022    0.660
##     lonely_Self      -1.090    0.145   -7.505    0.000   -1.223   -0.733
##     loner_Self       -1.231    0.147   -8.354    0.000   -1.382   -0.804
##     outgoing_Self     1.135    0.153    7.416    0.000    1.273    0.725
##     plain_Self       -0.879    0.140   -6.268    0.000   -0.987   -0.624
##     poor_Self        -0.712    0.139   -5.137    0.000   -0.799   -0.520
##     popular_Self      1.197    0.136    8.836    0.000    1.344    0.842
##     pushover_Self    -0.724    0.146   -4.961    0.000   -0.812   -0.503
##     shy_Self         -0.948    0.152   -6.238    0.000   -1.064   -0.621
##     social_Self       1.208    0.137    8.806    0.000    1.355    0.840
##     trendy_Self       1.117    0.133    8.431    0.000    1.254    0.810
##   agressive =~
##     agressive_Slf     1.000                               1.053    0.745
##     angry_Self        1.073    0.142    7.575    0.000    1.130    0.776
##     bossy_Self        1.012    0.146    6.934    0.000    1.066    0.715
##     contrllng_Slf     0.948    0.146    6.497    0.000    0.998    0.673
##     grumpy_Self       1.080    0.150    7.216    0.000    1.137    0.742
##     jealous_Self      0.806    0.139    5.818    0.000    0.849    0.607
##     lazy_Self         0.817    0.151    5.393    0.000    0.861    0.565
##     selfish_Self      0.950    0.138    6.884    0.000    1.001    0.710
##     snobby_Self       1.097    0.142    7.696    0.000    1.155    0.787
##     stubborn_Self     0.654    0.160    4.094    0.000    0.688    0.433
##   calm =~
##     calm_Self         1.000                               0.748    0.651
##     comfortng_Slf     1.071    0.215    4.985    0.000    0.801    0.574
##     considert_Slf     1.056    0.163    6.486    0.000    0.790    0.786
##     genuine_Self      1.098    0.177    6.206    0.000    0.821    0.743
##     giving_Self       1.204    0.197    6.096    0.000    0.900    0.727
##     helpful_Self      1.173    0.172    6.816    0.000    0.878    0.840
##     humble_Self       0.893    0.187    4.778    0.000    0.668    0.547
##     patient_Self      1.080    0.210    5.146    0.000    0.808    0.595
##     studious_Self     0.642    0.191    3.352    0.001    0.480    0.372
##   adventurous =~
##     adventurs_Slf     1.000                               1.233    0.826
##     daring_Self       0.993    0.128    7.786    0.000    1.225    0.824
##     risky_Self        0.671    0.121    5.554    0.000    0.828    0.583
##     rulefllwr_Slf    -0.171    0.118   -1.454    0.146   -0.211   -0.161
## 
## Covariances:
##   admired ~~
##     agressive        -0.087    0.131   -0.665    0.506   -0.073   -0.073
##     calm              0.341    0.112    3.058    0.002    0.407    0.407
##     adventurous       0.887    0.208    4.265    0.000    0.641    0.641
##   agressive ~~
##     calm             -0.372    0.113   -3.305    0.001   -0.473   -0.473
##     adventurous       0.319    0.161    1.979    0.048    0.246    0.246
##   calm ~~
##     adventurous       0.216    0.116    1.859    0.063    0.234    0.234
## 
## Variances:
##     admired_Self      0.952    0.146                      0.952    0.431
##     attractiv_Slf     0.836    0.127                      0.836    0.457
##     awkward_Self      1.534    0.230                      1.534    0.544
##     boring_Self       1.447    0.215                      1.447    0.641
##     confident_Slf     0.625    0.102                      0.625    0.252
##     cool_Self         0.977    0.149                      0.977    0.433
##     depressed_Slf     1.300    0.198                      1.300    0.454
##     flirty_Self       1.381    0.208                      1.381    0.521
##     insecure_Self     1.153    0.179                      1.153    0.375
##     leader_Self       1.349    0.202                      1.349    0.564
##     lonely_Self       1.290    0.196                      1.290    0.463
##     loner_Self        1.048    0.163                      1.048    0.354
##     outgoing_Self     1.461    0.221                      1.461    0.474
##     plain_Self        1.526    0.227                      1.526    0.610
##     poor_Self         1.726    0.254                      1.726    0.730
##     popular_Self      0.739    0.118                      0.739    0.290
##     pushover_Self     1.951    0.287                      1.951    0.747
##     shy_Self          1.800    0.268                      1.800    0.614
##     social_Self       0.766    0.122                      0.766    0.294
##     trendy_Self       0.825    0.129                      0.825    0.344
##     agressive_Slf     0.888    0.147                      0.888    0.444
##     angry_Self        0.844    0.144                      0.844    0.398
##     bossy_Self        1.086    0.176                      1.086    0.489
##     contrllng_Slf     1.203    0.190                      1.203    0.547
##     grumpy_Self       1.056    0.174                      1.056    0.449
##     jealous_Self      1.236    0.190                      1.236    0.632
##     lazy_Self         1.581    0.240                      1.581    0.681
##     selfish_Self      0.984    0.159                      0.984    0.496
##     snobby_Self       0.818    0.141                      0.818    0.380
##     stubborn_Self     2.049    0.304                      2.049    0.812
##     calm_Self         0.762    0.120                      0.762    0.577
##     comfortng_Slf     1.309    0.201                      1.309    0.671
##     considert_Slf     0.386    0.068                      0.386    0.382
##     genuine_Self      0.546    0.092                      0.546    0.448
##     giving_Self       0.723    0.120                      0.723    0.472
##     helpful_Self      0.322    0.063                      0.322    0.295
##     humble_Self       1.047    0.159                      1.047    0.701
##     patient_Self      1.193    0.184                      1.193    0.646
##     studious_Self     1.434    0.212                      1.434    0.862
##     adventurs_Slf     0.708    0.176                      0.708    0.318
##     daring_Self       0.707    0.174                      0.707    0.320
##     risky_Self        1.328    0.212                      1.328    0.660
##     rulefllwr_Slf     1.677    0.244                      1.677    0.974
##     admired           1.259    0.293                      1.000    1.000
##     agressive         1.110    0.269                      1.000    1.000
##     calm              0.559    0.164                      1.000    1.000
##     adventurous       1.521    0.338                      1.000    1.000

Estimates of reliability vary below between the CFA and the alphas on the raw scales, but I’m not sure why.

##           admired agressive      calm adventurous     total
## alpha  0.45964396 0.8920895 0.8575059   0.5014409 0.7726160
## omega  0.04277806 0.8937439 0.8602169   0.6814479 0.7210046
## omega2 0.04277806 0.8937439 0.8602169   0.6814479 0.7210046
## omega3 0.01204349 0.8920503 0.8605021   0.7219464 0.3250974
## avevar 0.52161736 0.4619776 0.4119190   0.4590871 0.4872755

## 
## Reliability analysis   
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA == 
##     "PA1"]], check.keys = T)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean  sd
##       0.95      0.95    0.97      0.51  20 0.014  3.7 1.2
## 
##  lower alpha upper     95% confidence boundaries
## 0.93 0.95 0.98 
## 
##  Reliability if an item is dropped:
##                 raw_alpha std.alpha G6(smc) average_r S/N alpha se
## admired_Self         0.95      0.95    0.97      0.50  19    0.015
## attractive_Self      0.95      0.95    0.97      0.51  19    0.015
## awkward_Self-        0.95      0.95    0.97      0.51  20    0.015
## boring_Self-         0.95      0.95    0.97      0.51  20    0.015
## confident_Self       0.95      0.95    0.96      0.50  19    0.015
## cool_Self            0.95      0.95    0.97      0.50  19    0.015
## depressed_Self-      0.95      0.95    0.97      0.50  19    0.015
## flirty_Self          0.95      0.95    0.97      0.51  20    0.015
## insecure_Self-       0.95      0.95    0.97      0.50  19    0.015
## leader_Self          0.95      0.95    0.97      0.51  20    0.015
## lonely_Self-         0.95      0.95    0.97      0.50  19    0.015
## loner_Self-          0.95      0.95    0.97      0.50  19    0.015
## outgoing_Self        0.95      0.95    0.97      0.51  20    0.015
## plain_Self-          0.95      0.95    0.97      0.51  20    0.015
## poor_Self-           0.95      0.95    0.97      0.52  21    0.014
## popular_Self         0.95      0.95    0.97      0.50  19    0.015
## pushover_Self-       0.95      0.95    0.97      0.52  20    0.014
## shy_Self-            0.95      0.95    0.97      0.51  20    0.015
## social_Self          0.95      0.95    0.97      0.50  19    0.015
## trendy_Self          0.95      0.95    0.97      0.50  19    0.015
## 
##  Item statistics 
##                   n raw.r std.r r.cor r.drop mean  sd
## admired_Self    100  0.73  0.74  0.74   0.70  3.6 1.5
## attractive_Self 100  0.73  0.74  0.72   0.70  4.1 1.4
## awkward_Self-   100  0.73  0.72  0.71   0.69  3.4 1.7
## boring_Self-    100  0.66  0.65  0.64   0.61  4.2 1.5
## confident_Self   99  0.85  0.85  0.85   0.83  3.7 1.6
## cool_Self        99  0.74  0.74  0.74   0.71  3.8 1.5
## depressed_Self-  99  0.77  0.77  0.77   0.74  4.0 1.7
## flirty_Self      99  0.69  0.69  0.67   0.65  3.1 1.6
## insecure_Self-  100  0.82  0.82  0.81   0.80  3.5 1.8
## leader_Self     100  0.65  0.66  0.64   0.61  3.3 1.5
## lonely_Self-    100  0.77  0.77  0.76   0.74  3.8 1.7
## loner_Self-     100  0.82  0.82  0.81   0.79  3.9 1.7
## outgoing_Self   100  0.70  0.70  0.69   0.66  3.5 1.8
## plain_Self-      99  0.66  0.65  0.63   0.62  3.8 1.6
## poor_Self-      100  0.56  0.56  0.53   0.51  4.2 1.5
## popular_Self     99  0.83  0.83  0.83   0.80  3.3 1.6
## pushover_Self-   99  0.58  0.58  0.55   0.53  4.0 1.7
## shy_Self-       100  0.67  0.66  0.64   0.62  3.1 1.7
## social_Self     100  0.82  0.82  0.81   0.79  3.9 1.6
## trendy_Self      99  0.80  0.81  0.80   0.78  3.5 1.6
## 
## Non missing response frequency for each item
##                    1    2    3    4    5    6 miss
## admired_Self    0.13 0.08 0.23 0.28 0.17 0.11 0.00
## attractive_Self 0.07 0.05 0.17 0.28 0.29 0.14 0.00
## awkward_Self    0.18 0.12 0.10 0.26 0.20 0.14 0.00
## boring_Self     0.27 0.23 0.15 0.21 0.09 0.05 0.00
## confident_Self  0.11 0.14 0.18 0.22 0.20 0.14 0.01
## cool_Self       0.11 0.09 0.18 0.28 0.20 0.13 0.01
## depressed_Self  0.26 0.18 0.18 0.15 0.12 0.10 0.01
## flirty_Self     0.21 0.21 0.14 0.19 0.16 0.08 0.01
## insecure_Self   0.19 0.15 0.15 0.17 0.17 0.17 0.00
## leader_Self     0.14 0.22 0.17 0.22 0.16 0.09 0.00
## lonely_Self     0.22 0.16 0.19 0.21 0.10 0.12 0.00
## loner_Self      0.25 0.18 0.14 0.18 0.13 0.12 0.00
## outgoing_Self   0.19 0.14 0.14 0.15 0.22 0.16 0.00
## plain_Self      0.18 0.17 0.22 0.18 0.14 0.10 0.01
## poor_Self       0.29 0.15 0.22 0.14 0.17 0.03 0.00
## popular_Self    0.17 0.16 0.21 0.23 0.10 0.12 0.01
## pushover_Self   0.27 0.18 0.10 0.21 0.17 0.06 0.01
## shy_Self        0.14 0.12 0.13 0.19 0.20 0.22 0.00
## social_Self     0.11 0.11 0.13 0.26 0.19 0.20 0.00
## trendy_Self     0.15 0.16 0.13 0.28 0.18 0.09 0.01

## 
## Reliability analysis   
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA == 
##     "PA2"]], check.keys = T)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean  sd
##       0.89      0.89    0.91      0.45 8.3 0.031  2.7 1.1
## 
##  lower alpha upper     95% confidence boundaries
## 0.83 0.89 0.95 
## 
##  Reliability if an item is dropped:
##                  raw_alpha std.alpha G6(smc) average_r S/N alpha se
## agressive_Self        0.88      0.88    0.89      0.44 7.2    0.035
## angry_Self            0.87      0.87    0.88      0.43 6.9    0.036
## bossy_Self            0.88      0.88    0.89      0.45 7.2    0.035
## controlling_Self      0.88      0.88    0.89      0.45 7.3    0.035
## grumpy_Self           0.88      0.88    0.89      0.45 7.2    0.035
## jealous_Self          0.89      0.89    0.90      0.47 7.9    0.033
## lazy_Self             0.89      0.89    0.90      0.47 8.0    0.033
## selfish_Self          0.88      0.88    0.89      0.45 7.3    0.035
## snobby_Self           0.87      0.87    0.89      0.44 7.0    0.035
## stubborn_Self         0.90      0.90    0.91      0.49 8.6    0.032
## 
##  Item statistics 
##                    n raw.r std.r r.cor r.drop mean  sd
## agressive_Self    99  0.76  0.76  0.74   0.69  2.3 1.4
## angry_Self       100  0.81  0.81  0.81   0.75  2.5 1.5
## bossy_Self       100  0.75  0.75  0.73   0.67  2.6 1.5
## controlling_Self 100  0.74  0.74  0.71   0.66  2.6 1.5
## grumpy_Self       99  0.74  0.75  0.72   0.67  2.6 1.5
## jealous_Self     100  0.63  0.63  0.58   0.53  2.9 1.4
## lazy_Self         99  0.63  0.62  0.56   0.52  2.6 1.5
## selfish_Self      99  0.74  0.75  0.72   0.67  2.6 1.4
## snobby_Self       99  0.79  0.79  0.77   0.73  2.3 1.5
## stubborn_Self    100  0.54  0.53  0.45   0.42  3.5 1.6
## 
## Non missing response frequency for each item
##                     1    2    3    4    5    6 miss
## agressive_Self   0.42 0.16 0.19 0.12 0.08 0.02 0.01
## angry_Self       0.34 0.24 0.17 0.15 0.05 0.05 0.00
## bossy_Self       0.32 0.22 0.16 0.17 0.09 0.04 0.00
## controlling_Self 0.29 0.29 0.12 0.17 0.09 0.04 0.00
## grumpy_Self      0.29 0.26 0.14 0.15 0.11 0.04 0.01
## jealous_Self     0.24 0.14 0.28 0.20 0.10 0.04 0.00
## lazy_Self        0.31 0.24 0.12 0.19 0.08 0.05 0.01
## selfish_Self     0.28 0.24 0.16 0.19 0.10 0.02 0.01
## snobby_Self      0.43 0.20 0.09 0.17 0.08 0.02 0.01
## stubborn_Self    0.15 0.13 0.22 0.20 0.18 0.12 0.00

## 
## Reliability analysis   
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA == 
##     "PA3"]], check.keys = T)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd
##       0.86      0.87    0.88      0.42 6.6 0.037  4.5 0.84
## 
##  lower alpha upper     95% confidence boundaries
## 0.79 0.86 0.93 
## 
##  Reliability if an item is dropped:
##                  raw_alpha std.alpha G6(smc) average_r S/N alpha se
## calm_Self             0.84      0.85    0.85      0.41 5.7    0.043
## comforting_Self       0.86      0.86    0.87      0.44 6.3    0.040
## considerate_Self      0.83      0.84    0.85      0.40 5.3    0.043
## genuine_Self          0.84      0.84    0.85      0.41 5.4    0.043
## giving_Self           0.84      0.85    0.86      0.42 5.7    0.042
## helpful_Self          0.83      0.84    0.84      0.40 5.3    0.043
## humble_Self           0.85      0.86    0.87      0.43 6.1    0.041
## patient_Self          0.85      0.86    0.86      0.43 6.1    0.041
## studious_Self         0.87      0.87    0.88      0.46 6.9    0.039
## 
##  Item statistics 
##                    n raw.r std.r r.cor r.drop mean  sd
## calm_Self         99  0.73  0.74  0.70   0.65  4.4 1.2
## comforting_Self  100  0.63  0.62  0.55   0.50  4.2 1.4
## considerate_Self 100  0.79  0.81  0.79   0.73  4.8 1.0
## genuine_Self     100  0.77  0.78  0.75   0.69  4.7 1.1
## giving_Self      100  0.72  0.72  0.68   0.62  4.6 1.3
## helpful_Self     100  0.80  0.81  0.80   0.74  4.8 1.1
## humble_Self      100  0.65  0.65  0.58   0.53  4.4 1.2
## patient_Self      99  0.67  0.66  0.61   0.55  4.1 1.3
## studious_Self    100  0.52  0.51  0.41   0.37  4.4 1.3
## 
## Non missing response frequency for each item
##                     1    2    3    4    5    6 miss
## calm_Self        0.01 0.07 0.10 0.28 0.35 0.18 0.01
## comforting_Self  0.06 0.09 0.08 0.35 0.24 0.18 0.00
## considerate_Self 0.00 0.02 0.09 0.25 0.34 0.30 0.00
## genuine_Self     0.00 0.04 0.08 0.29 0.29 0.30 0.00
## giving_Self      0.01 0.10 0.03 0.31 0.28 0.27 0.00
## helpful_Self     0.00 0.04 0.06 0.27 0.34 0.29 0.00
## humble_Self      0.04 0.02 0.15 0.31 0.29 0.19 0.00
## patient_Self     0.03 0.12 0.13 0.27 0.28 0.16 0.01
## studious_Self    0.02 0.07 0.13 0.31 0.24 0.23 0.00

## 
## Reliability analysis   
## Call: alpha(x = dataCFA[, itemScaleGroupsCFA$item[itemScaleGroupsCFA$maxPA == 
##     "PA4"]], check.keys = T)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean  sd
##       0.72      0.71    0.73      0.38 2.4 0.082  3.2 1.1
## 
##  lower alpha upper     95% confidence boundaries
## 0.55 0.72 0.88 
## 
##  Reliability if an item is dropped:
##                    raw_alpha std.alpha G6(smc) average_r S/N alpha se
## adventurous_Self        0.66      0.66    0.58      0.39 1.9    0.108
## daring_Self             0.50      0.50    0.47      0.25 1.0    0.126
## risky_Self              0.60      0.59    0.64      0.33 1.5    0.112
## rulefollower_Self-      0.79      0.78    0.73      0.55 3.6    0.091
## 
##  Item statistics 
##                      n raw.r std.r r.cor r.drop mean  sd
## adventurous_Self   100  0.73  0.72  0.65   0.49  4.0 1.5
## daring_Self        100  0.87  0.86  0.85   0.73  3.2 1.5
## risky_Self         100  0.79  0.78  0.66   0.58  2.9 1.4
## rulefollower_Self- 100  0.54  0.56  0.34   0.25  2.7 1.4
## 
## Non missing response frequency for each item
##                      1    2    3    4    5    6 miss
## adventurous_Self  0.07 0.14 0.12 0.23 0.31 0.13    0
## daring_Self       0.17 0.16 0.16 0.34 0.10 0.07    0
## risky_Self        0.21 0.22 0.23 0.18 0.12 0.04    0
## rulefollower_Self 0.04 0.08 0.11 0.29 0.27 0.21    0

What conclusions can we draw? The CFA indicates that we could do better in this model. But the scale alphas coefficients are very good, with even the 4 item adventurous factor getting >.7. However, there are a lot of cross loadings in the EFA, and we totally ignore those, which is why the CFA fit is so shabby. This can especially be the case with many items per scale.